Question: GRADE 12 MATHEMATICAL LITERACY PORTFOLIO TASK
QUESTION 2
The local community decided to import the tanks from overseas. They used the following refrigerated shipping container with the dimensions to place the tanks inside.
STORAGE VOLUME: 108.13 m³
(3.52m × 2.56m × 12m)
COMPRESSOR UNIT AREA:
6.52 m² (2.56m × 2.55m)
h = 3.52 m
w = 2.56 m
l = 12 m
Use the diagram above to answer the questions that follow:
2.1 Calculate the surface area (in m²) of the refrigerated container. (5)
You may use:
Surface Area = 2(length x width) + 2 (length x height) = 2(width x height) – area needed for the compressor
1. **State the problem:** Calculate the surface area of the refrigerated container given dimensions $h=3.52$ m, $w=2.56$ m, $l=12$ m, and subtract the compressor unit area $6.52$ m².
2. **Formula used:** The surface area formula given is:
$$\text{Surface Area} = 2(l \times w) + 2(l \times h) + 2(w \times h) - \text{compressor area}$$
Note: The problem states $= 2(l \times w) + 2(l \times h) = 2(w \times h) - \text{compressor area}$ but this seems incomplete. The total surface area of a rectangular prism is:
$$2(lw + lh + wh)$$
We will calculate total surface area and then subtract compressor area.
3. **Calculate each area:**
- $l \times w = 12 \times 2.56 = 30.72$
- $l \times h = 12 \times 3.52 = 42.24$
- $w \times h = 2.56 \times 3.52 = 9.0112$
4. **Calculate total surface area:**
$$2(30.72 + 42.24 + 9.0112) = 2(81.9712) = 163.9424$$
5. **Subtract compressor area:**
$$163.9424 - 6.52 = 157.4224$$
6. **Final answer:**
The surface area of the refrigerated container is approximately
$$\boxed{157.42 \text{ m}^2}$$